## 16 Citations

Non-coboundary Poisson–Lie structures on the book group

- Mathematics
- 2012

All possible Poisson–Lie (PL) structures on the 3D real Lie group generated by a dilation and two commuting translations are obtained. Their classification is fully performed by relating these PL…

Integrable deformations of the Bogoyavlenskij-Itoh Lotka-Volterra systems

- Mathematics
- 2016

Given a constant skew-symmetric matrix A, it is a difficult open problem whether the associated Lotka-Volterra system is integrable or not. We solve this problem in the special case when A is a…

A new class of integrable Lotka–Volterra systems

- MathematicsJournal of Computational Dynamics
- 2019

A parameter-dependent class of Hamiltonian (generalized) Lotka-Volterra systems is considered. We prove that this class contains Liouville integrable as well as superintegrable cases according to…

Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System

- Mathematics
- 2017

Integrable deformations of an integrable case of the Rikitake system are constructed by modifying its constants of motions. Hamilton-Poisson realizations of these integrable deformations are given.…

Quantum algebras as quantizations of dual Poisson–Lie groups

- Mathematics
- 2013

A systematic computational approach for the explicit construction of any quantum Hopf algebra (Uz(g), Δz) starting from the Lie bialgebra (g, δ) that gives the first-order deformation of the…

Poisson–Hopf algebra deformations of Lie–Hamilton systems

- Mathematics
- 2017

Hopf algebra deformations are merged with a class of Lie systems of Hamiltonian type, the so-called Lie–Hamilton systems, to devise a novel formalism: the Poisson–Hopf algebra deformations of…

Variational discretization for the planar Lotka–Volterra equations in the Birkhoffian sense

- Mathematics
- 2016

In this paper, we derive the variational characterization of the planar Lotka–Volterra equations in the Birkhoffian sense and ulteriorly construct variational integrators for the group of equations.…

Classification of real three-dimensional Poisson–Lie groups

- Mathematics
- 2012

All real three-dimensional Poisson–Lie (PL) groups are explicitly constructed and fully classified under group automorphisms by making use of their one-to-one correspondence with the complete…

On the Integrable Deformations of the Maximally Superintegrable Systems

- MathematicsSymmetry
- 2021

This paper alters the constants of motion, and using these new functions, construct a new system which is an integrable deformation of the initial system, and new maximally superintegrable systems are obtained.

## References

SHOWING 1-10 OF 23 REFERENCES

Hamiltonian structure and Darboux theorem for families of generalized Lotka–Volterra systems

- Mathematics
- 1998

This work is devoted to the establishment of a Poisson structure for a format of equations known as generalized Lotka–Volterra systems. These equations, which include the classical Lotka–Volterra…

Families of invariants of the motion for the Lotka–Volterra equations: The linear polynomials family

- Mathematics
- 1992

The modified Carleman embedding method already introduced by the authors to find first integrals (invariants of the motion) of polynomial form to the Lotka–Volterra system is described in detail, and…

A systematic construction of completely integrable Hamiltonians from coalgebras

- Mathematics
- 1998

A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir elements is presented. In particular,…

Integrable systems and loop coproducts

- Mathematics
- 2010

We present a generalization of a framework for the construction of classical integrable systems that we call loop coproduct formulation (Musso 2010 J. Phys. A: Math. Theor. 43 434026). In this paper,…

Darboux integrability for 3D Lotka-Volterra systems

- Mathematics
- 2000

We describe the improved Darboux theory of integrability for polynomial ordinary differential equations in three dimensions. Using this theory and computer algebra, we study the existence of first…

Poisson structure of dynamical systems with three degrees of freedom

- Mathematics
- 1993

It is shown that the Poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one‐form in three dimensions. Advantage is taken of this fact and…